Solve for $x$ and $y$ using elimination. $\begin{align*}5x+y &= 7 \\ 4x-y &= 8\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $9x = 15$ Divide both sides by $9$ and reduce as necessary. $x = \dfrac{5}{3}$ Substitute $\dfrac{5}{3}$ for $x$ in the top equation. $5( \dfrac{5}{3})+y = 7$ $\dfrac{25}{3}+y = 7$ $y = -\dfrac{4}{3}$ $y = -\dfrac{4}{3}$ The solution is $\enspace x = \dfrac{5}{3}, \enspace y = -\dfrac{4}{3}$.